U.K. Neutrino Factory Target Studies

Introduction

There are proposals [1] to build a Neutrino Factory in the US, Europe and Japan, in
order to understand some of the basic properties of neutrinos.
The Neutrino Factory will consist of a proton driver accelerator delivering short
pulses of beam to a heavy metal target at GeV energies at up to ~50 Hz, with a mean
power of ~4 MW.
As a result of the beam interaction with the target, a number of pions will be
produced, as well as other secondary products.
The pions decay to muons which are focussed and accelerated to tens of GeV.
The muons then circulate in a large storage/decay ring with long straight sections
where they decay to neutrinos.
The neutrinos come off in a narrow cone along the axis of the muon beam and the
arms of the decay ring are directed at suitable neutrino detectors many kilometres
distant.

To learn more about U.K. Neutrino Factory project try one of the following links:

Solid Target for a Neutrino Factory

The target in the Neutrino Factory forms the most likely showstopper in the project
and hence R&D in this area is particularly important.
Because of the high energy density dissipated in the target and difficulties in
removing the heat, it has been proposed to use moving liquid and solid metal targets.
A free mercury jet [2] has the advantages of not suffering from radiation damage and
being capable of dissipating in excess of 1 MW.
The MERIT experiment [3] will be run at CERN to test the principle and examine any
problems.
In solid target case, when a pulse from the proton driver hits the target, it will
cause a temperature rise of up to 200 K in a few hundred ns.
This will create two main problems:

Without an efficient cooling system for a stationary target or a mechanism for
changing the target between pulses, the target will become very hot, very quickly.
Solid targets in the form of a rotating metal band [4,5] have been suggested.
In this case we bring the same section of target into the beam every 3 s and, but
even though it is cooled by radiation, the band will reach a steady state temperature
of 2000 K.

It will create a sudden thermal expansion in the centre of the target that will
in turn create a stress or shock wave to pass through the material, reflect off the
outer surface and oscillate for many 10's of microseconds (Figure 1).
Simple calculations suggest that the maximum stress will exceed the yield strength of
tantalum at 2000 K, for example.
As well as these two problems, the target will also become extremely active and
suffer very serious radiation damage. The radiation damage means that using a target
that depends on some special property of material is risky as this property is
unlikely to last very long.

Our efforts have been concentrated on the problem of shock in solid targets.
The work we have done is described in the following sections.
Note that although focussed on the Neutrino Factory, much of this work is directly
relevant for other projects requiring high power targets, in particular the T2K
experiment (Phase I and Phase II).

Shock studies

Shock is the main issue for solid targets and an experimental programme was required
to assess the lifetime of different solids in a Neutrino Factory, benchmark models
of shock in solids under the appropriate conditions and gain a better theoretical
understanding of this phenomenon.
The main difficultly for such a programme is producing a shock equivalent to that
from the Neutrino Factory proton beam in the same manner as the protons would,
without building the proton driver. The energy density from this will be about
300 J/cm3 averaged over the target.
As a result, we devised a technique using a high current power supply.
If a sufficiently large current in a sufficiently short pulse is passed through a
small enough diameter conductor, the current will penetrate to the centre of the
conductor in a time which is short compared to the speed of sound in the material.
In this way, a shock can be induced which looks not unlike the heating from a proton
beam at the centre.
Results from a study [6,7] using LS-DYNA [8] show that a 8 kA pulse at
50 kV which has a rise time of about 100 ns and a total pulse length
of 800 ns will achieve our aims.
A thin wire is necessary to allow the current to diffuse into the centre of the wire
in a sufficiently short time for the shock to be effective.
For tantalum and tungsten the wire cannot be greater than ~0.5 mm in diameter.

A power supply for the ISIS [9] kicker magnets is being used, supplying a maximum
of 60 kV and 10000 A at up to 50 Hz in a pulse which rises in
100 ns and is 800 ns long.
The wires, of 3-4 cm length, are supported in a vacuum chamber to avoid
oxidation.
One end of the wire is firmly clamped and the other end is allowed to expand
(Figure 2) freely through a pair of graphite (or copper) conductors which lightly
clamp the wire.

Figure 1: The shock (radial stress) wave created in a tantalum target by the Neutrino
Factory proton beam.
It is shown for a pulse of 10 bunches of different lengths (see the LS-DYNA
Studies section below).

The wire is operated at temperatures of 1600-2000 K by adjusting the pulse
repetition rate.
The temperature is measured by a manually operated optical pyrometer
and an electronic pyrometer, which can measure at up to 1 kHz rate, allowing the
pulse temperature to be measured.
The current through the wire is measured by a current transformer.
By calculating the Ohmic heating the temperature rise can be cross checked to the
electronic pyrometer measurement.
Note that the current also produces a magnetic field which squeezes the wire,
inducing an additional stress. Both the effect from the heating of the wire
(the thermal shock) and the magnetic effect (the Lorenz shock) are included in
the LS-DYNA simulations (Figure 3).

Figure 2: A tantalum wire under test

The power supply was initially run at 5 kA with tantalum, giving a
100 K temperature rise per pulse.
This creates a stress equivalent to 2 MW proton beam in the Neutrino Factory
target.
The tests with tantalum achieved a lifetime of only 2x105 pulses, much
less than the 3.3x106 required for one years running with each
tantalum sample being in the beam every 3 s.
Repeated tests always show basically the same failure mode.
A qualitative understand of this has been achieved from LS-DYNA.
As a result, we have proved that tantalum is simply too weak at 2000 K and
hence a sample of tungsten was tested as this known to be stronger at these
high temperatures.

Figure 3: Radial stress at the axis of the wire due to thermal (dotted line) and Lorenz forces (dashed line).

The results of a number of tests with 0.5 mm diameter tantalum and tungsten
wires are summarised in Table 1.
As we already said, the tantalum was too weak at temperatures of 1400 K or more
necessary for the radiant heat dissipation and only one typical result is shown in
the table.
The tungsten was much more robust and most of the failures occurred in the end
connections rather than the wire.
In fact the wire only failed when operated at temperatures well over ~2000 K.

Table 1. Results of some tantalum and tungsten wire tests.
Only one representative tantalum wire test is shown. The "Equivalent Target"
columns show the equivalent beam power for a full size target of 2 and 3 cm
diameter for the same stress in the test wire.
(Assumes a parabolic beam distribution, 3 micro-pulses per macro-pulse of
~20&nbspμs
and beam diameter equal to target diameter.)

#

Wire Material

Current

Pulse Temp

Peak Temp

Number of Pulses

Equivalent Target

Beam Power

Target Diameter

A

K

K

Millions

MW

cm

1

TANTALUM

3000

60

1800

0.2

-

-

TUNGSTEN

2

Broke when increased to 7200 A (2200 K)

4900

90

2000

>3.4

2

2

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

4

3

3

Stuck to top copper conductors

6400

150

1900

>1.6

4

2

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

8

3

4

Not broken

5560

120

1900

4.2

3

2

&nbsp

Top connector failed

5840

130

2050

>9.0

6

3

5

Stuck to top copper conductors

7000

180

1950

>1.2

4

2

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

&nbsp

8

3

The "Equivalent Target" values were calculated in the following way.
As well as giving the pion flux, MARS [10] has been used here to determine the
energy deposition in the target as a function of position.
From this the temperature rise can be calculated.
The temperature rises are then used in the LS-DYNA programme to calculate the
dynamic stresses in the target.
The stress in the wire is calculated including both temperature and the Lorenz
force from the magnetic field produced by the current on itself.
Hence it is possible to relate the current in the wire that produces the same
peak stress in the full sized target.

The lifetime tests currently only induce radial and longitudinal oscillations in
the wire.
Experience from other target tests suggest that so-called "violin modes",
corresponding to the beam passing through the target at an angle, may also be
very important.
It has been calculated that, for example, for the Neutrino Factory target with an
off axis beam (displaced by 5 mm in a 10 mm radius target) the stress
is increased by ~25%.
It is planned to modify the experiment to induce and study these modes as well,
by using two parallel wires carrying a current.
Figure 4 shows the calculated additional stress for two parallel wires separated
by a distance d carrying a pulse current I.

Figure 4. Additional stress in two parallel wires carrying a pulse current I
separated by a distance d.

LS-DYNA Studies

As indicated in the previous section, LS-DYNA simulations have been used both to
plan and to understand the experimental tests of solid target lifetime.
In addition, LS-DYNA has been used to investigate methods of reducing the shock in
a solid target. These studies have focussed on two items: the bunch structure of
the proton beam and the size of the target with respect to the beam size.
The effect of the bunch structure is shown in Figure 1 and in more detail in
Figure 5.

What has been studied is the effect of splitting a single bunch from the proton
driver into a number of separate bunches.
If these separate bunches are in a pulse which has a length which is comparable to
the characteristic time of the target, the time it takes the shock to pass through it,
then there is little reduction in the shock.
However, if the separation between the bunches is long with respect to this time,
then the effect of each bunch becomes independent and the overall shock is reduced
by the number of bunches.
Note that the stress passes both radially and longitudinally through the material.
Although the radial stress is the biggest, there is an interference between these two.
It is this interference that leads to the peaks in the figure.
With the Neutrino Factory there is a requirement for short micro-pulses of 1-2 ns
length within a macro-pulse of a few micro-seconds.
An odd number of micro-pulses is preferred for the muon accelerator and the more
micro-pulses the easier for the proton driver with regard to space charge.
As a result, a possible design is for a proton beam of 3 or 5 micro-pulses spaced
apart by 5-10 μs. It should be noted that it is against this number
that the experimental work described in the previous section has been compared.

So, designers of the proton driver have indicated that splitting the beam into 3
(5) bunches, each 2 ns long, in a pulse of 30-40 μs should be possible.
In this configuration, the maximum von Mises stress, the most important for the
target, is about 300 MPa for our default target configuration (2 cm
in diameter, ~20 cm in length).
The effect of increasing the target size with respect to the beam size has also
been studied.
This shows that if the target is at least twice the radius of the beam, the
additional material reduces the shock.
There is a problem with doing this, however: the rate of re-absorption of the pions
increases due to this additional material and the pion flux drops dramatically.
As a result, we are taking the alternative approach of increasing both the beam
size and the target size.
So, we are able to reduce a shock by simply reducing the peak energy density in
the target.
An increase in diameter from 2 to 3 cm (see Figure 5) would bring a factor of
2 reduction in stress.
The potential problem is, again, that the increase in material would bring a
reduction in pion production due to re-absorption.
However, studies performed with MARS indicate that the loss is only 5% and this
may be recovered by increasing the target length (let's say from 20 to 25 cm).

We have also looked for either stronger materials or materials in which the shock
is smaller than in tungsten.
The thermal stress in the target is determined by the coefficient of thermal
expansion &alpha (i.e. the amount it expands) and the elastic modulus E
(i.e. its response), as follows:

ST ~ αEΔT/(1 - &nu)

where ΔT = Ed/Cp is
the temperature rise, &nu is Poisson's ratio, Ed is the
density of the energy deposition in the wire and Cp is
the specific heat.
Note that α, E, &nu and Cp are all temperature
dependent and LS-DYNA is used to model
for different materials under the Neutrino Factory target conditions.
If the tensile strength is used as a measure of the mechanical strength of a
material, then we can use the ratio of the thermal stress to the tensile strength
as a quality factor for the material.
The smaller this factor is, the better the material as a target.
To achieve this requires one or more of a small coefficient of thermal expansion
or a small elastic modulus to reduce the stress (e.g. graphite) or a large
tensile strength (for example tantalum + 10% tungsten and tungsten + 25% rhenium).
We plan to study these materials to see if they are really better than tungsten
under such extreme conditions.
In addition to this, a type of laser interferometer called a VISAR [11] has
been ordered to make measurements of the surface acceleration of the wire.
This will be compared with the predictions of LS-DYNA to ensure that our
interpretation of the results seen is correct. Samples of tantalum and tungsten are
also currently being irradiated in the Brookhaven National Laboratory to ensure
that the material properties we are relying on, in particular tensile strength,
are not adversely affected too much by radiation damage.
In addition, tungsten has replaced tantalum in the ISIS target at RAL.
The first target has been changed recently after suffering radiation damage of
12 dpa without failing.
As an individual Neutrino Factory target will receive damage at a similar level,
this is further positive evidence of the feasibility of a tungsten target.
More results and details about our modelling studies can be found on the
following UK Neutrino Factory web page:
http://hepunx.rl.ac.uk/uknf/wp3/shocksims.

Conclusions

During this initial phase of studying thermal shock in materials that are candidates
for a Neutrino Factory target we have:

developed a much better understanding of shock in solid targets using LS-DYNA
simulations,

through this, identified methods by which the shock can be reduced,

built a system for delivering sufficient shock in a manner very similar to a
Neutrino Factory proton beam,

using this, demonstrated that our original material candidate, tantalum, is
not strong enough at 2000 K,

demonstrated that in our standard configuration, tungsten has a sufficient
lifetime when subjected to the radial and longitudinal shock from a
4 MW beam,

demonstrated that by increasing the size of the target and beam, this limit can
be extended above the required 4 MW without significant loss in the
captured pion flux,

provided an initial demonstration of the feasibility of a solid target for a
Neutrino Factory.

Although some of the checks are still to be made, our conclusion is this work has
given the first ever demonstration that a solid target may have sufficient
lifetime due to shock in a multi-megawatt proton beam for neutrino production.